President Obama plans to push Congress to move quickly in the coming months on an ambitious overhaul of the immigration system that would include a path to citizenship for most of the 11 million illegal immigrants in the country, senior administration officials and lawmakers said last week.

Mr. Obama and Senate Democrats will propose the changes in one comprehensive bill, the officials said, resisting efforts by some Republicans to break the overhaul into smaller pieces — separately addressing young illegal immigrants, migrant farmworkers or highly skilled foreigners — which might be easier for reluctant members of their party to accept.